Tony HoffmanIncredible Numbers by Professor Ian Stewart (for iPad)Incredible Numbers is an interactive iPad app that sheds light on some important concepts to help students and laypeople alike increase their appreciation of mathematics.

Focuses on important and fascinating mathematical concepts. Interactive exercises. Biographical sketches of mathematicians mentioned in the text.

Cons

Some interactive features were not very responsive in testing. Navigation could be improved. Somewhat pricey for an iPad app.

Bottom Line

Incredible Numbers is an interactive iPad app that sheds light on some important concepts to help students and laypeople alike increase their appreciation of mathematics.

Incredible Numbers by Professor Ian Stewart ($9.99) is an interactive iPad app that tackles some important areas of mathematics in a systematic and lucid way. Created by a math professor and prolific writer, it is full of essays, interactive exercises, bios of mathematicians, and puzzles. Although it helps to have had at least some high school math to get the most out of the app, much of it is accessible to the average person. It's a good educational tool to increase one's appreciation of mathematics, although it's a bit expensive for an iPad app, and its navigation could be improved.

From Pi to Polygons
The app can run on an iPad running iOS 7.0 or later. I tested it with an iPad Air 2 to take advantage of the device's large screen. Incredible Numbers is the brainchild of Professor Ian Stewart, the author of numerous research papers and popular mathematics books, and an authority on mathematical recreations and puzzles. It consists of 23 essays, grouped into eight topics of interest to mathematicians that will also appeal to many laymen. On the Home page, the names of the topicsPrimes, Secret Codes, Infinity, Factorials!, Nature, Music, π = 3.141592 , and Polygonsappear within circles, each a different color, arranged in an oval configuration. A smaller, ninth circle, labeled Puzzles, lies just outside the oval.

At the upper- and lower-left corners of the Home page are touch-sensitive icons. The top-left icon, three stacked horizontal lines, takes you to the About page, which discusses the app's intent and how it was created. At the top-left corner of the About page is a menu with tabs for About, Professsor Ian Stewart, Profile Books, Touchpress, and Credits. The Home page's bottom-left link, a capital P, opens the page for Profile Books, which partnered with Touchpress in the creation of the app. The menu items are the same as for the previous button. At the Home page's bottom right is a button titled Touchpress, which lets you follow the company on Facebook or Twitter, or get on its email list. It also has a cool animated video highlighting the press's Molecules app. At the Home Page's upper right is a Share icon, which lets you share the link to the Incredible Numbers iTunes page on Twitter or Facebook, or email it.

Sections
Tapping on one of the section titles takes you to a section page, which includes the section title, a few introductory sentences, and then links to the articles within the section. In the case of the Primes sections, you get links titled Patterns and Primes, Finding Factors, and Hunting for Primes. Tapping on one of these links takes you to the article in question. At the bottom of the article is a link to the next article. At the bottom of the last article in the section is a link to the next section.

The Primes section explores the nature of prime numbers, and mathematicians' centuries-old fascination with them. Most mathematicians' names appearing in the articles link to a page with a few-paragraphs-long biographical sketch of the person in question (Euclid, for example). Each article contains several interactive features (the entire app includes 71 interactive exercises), in which you drag on a highlighted area of the screen to activate them. In one, you can make the sequence of prime numbers expand or contract, while another shows factorizations of the numbers between 2 and 200. For example, an 8 is shown with lines branching down to its factors, 2 and 4, while 4 in turn branches down to 2 and 2. A number like 7, which has no factors, is labeled as Prime.

A bar along the right-hand edge of the screen, its color matching the section you're in, indicates a full-screen exercise that you can access by swiping the bar toward the left. In the section on pi, swiping on the bar reveals a grid depicting the first million digits of pi (although only several hundred appear on screen at once). You are then prompted to enter the digits of your birthday, in the form DDMMYY, to see if they appear in order anywhere within the first million digits of pi. (Mine did, starting at the 167,251st digit of pi. My birthday digits then appeared highlighted within the grid, complete with the digits that surround them).

Secret Codes to Sunflowers
Among my favorite sections are Secret Codes and Nature. Secret Codes includes an article on the German World War II Enigma Machine, how its code was structured, and how it was broken by Alan Turing and his team of Bletchley Park cryptologists. There's a full-page exercise available that's a virtual replica of the Enigma Machine on which you can encode and decode messages.

The Nature section highlights the Fibonacci sequence, and shows how a spiral derived from its numbers closely matches the Golden spiral found in nature. The exercise in which you construct the spiral is fun, as is the one showing how seeds within a sunflower naturally form a pattern in which they're nearly evenly spaced and form spirals, and the angle at which they're arranged closely matches the Fibonacci sequence. In the exercise, you can alter the angle by running your finger around the virtual sunflower and look for other stable angles.

Puzzles From a Master
The Puzzles section includes 15 of Stewart's own math puzzles, some of which you can try solving on screen. I was able to figure out maybe a third of them; for the rest, I cheated and clicked the Answer link at the bottom. My only regret is that there weren't more puzzles.

Using the app heightened my appreciation of both abstract math and mathematics in everyday life, and helped me to reconnect with some long-forgotten mathematical conceptsmy last math class was high school calculus, close to 40 years ago. (More recently, I did production work on a math magazine, The Mathematical Intelligencer, for which Professor Stewart served as European Editor, one of the main reasons I selected this app to test.) Although some of the app's essays are clear and understandable, others are over my head. For example, in the Polygons exercise, I found it very hard to follow along with the drawing of a 17-sided figureusing a virtual ruler and compassa based on a formula, crawling with square roots, devised by the great mathematician Carl Friedrich Gauss.

Although my rusty high-school math wasn't always up to the task of fully understanding some of the more intricate mathematics, I could grasp the basic concepts. I came away from testing this app a little more knowledgeable about the subject areas it covered, with a greater respect for mathematicians, and more curious about some of the concepts that were covered as well as about mathematics in general.

Quirks and Quibbles
In testing the app, I came across one design shortcoming, as well as problems with a few particular features. The individual sections bear no direct connection to each other, and are arranged somewhat randomly. If you're not interested in the next section, or if you just want to leave the one you're in, you can get back to the Home page by using a back-arrow link at the screen's upper left. Depending on what page you're on, it can take up to three taps to get to Home. I would have liked to have seen a Home button on each page, or a pull-down menu allowing you to move between the sections.

Some interactive features were not very responsive in testing. For instance, in one puzzle, you need to tap a circle that contains a number to highlight the number, and then tap a second circle to move the number there. I often had to tap the circle many times to get it to respond.

Conclusion
I see the Incredible Numbers iPad app as both a teaching and a math-appreciation tool. It's easy to recommend for high school or college students, as well as anyone looking to improve their grasp of some important mathematical concepts andin some casesto see how mathematics intersects with everyday life. The app's interactive nature gives it a dimension lacking in math textbooks. I didn't fully understand some of the material that was presented, but that didn't take away from my appreciation of the general concepts. Above all, I was left with the thought that math is beautiful, math is vital, and it is worth the work it takes to better comprehend it.

About the Author

As Analyst for printers, scanners, and projectors, Tony Hoffman tests and reviews these products and provides news coverage for these categories. Tony has worked at PC Magazine since 2004, first as a Staff Editor, then as Reviews Editor, and more recently as Managing Editor for the printers, scanners, and projectors team.
In addition to editing, T... See Full Bio

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